Fractal Geometry-Based Decrease in Trimethoprim-Sulfamethoxazole Concentrations in Overweight and Obese People

R G Hall Nd, J G Pasipanodya, C Meek, R D Leff, M Swancutt, T Gumbo, R G Hall Nd, J G Pasipanodya, C Meek, R D Leff, M Swancutt, T Gumbo

Abstract

Trimethoprim-sulfamethoxazole (TMP-SMX) is one of the most widely drugs on earth. The World Health Organization recommends it as an essential basic drug for all healthcare systems. Dosing is inconsistently based on weight, assuming linear relationships. Given that obesity is now a global "pandemic" it is vital that we evaluate the effect of obesity on trimethoprim-sulfamethoxazole concentrations. We conducted a prospective clinical experiment based on optimized design strategies and artificial intelligence algorithms and found that weight and body mass index (BMI) had a profound effect on drug clearance and volume of distribution, and followed nonlinear fractal geometry-based relationships. The findings were confirmed by demonstrating decreased TMP-SMX peak and area under the concentration-time curves in overweight patients based on standard regression statistics. The nonlinear relationships can now be used to identify new TMP-SMX doses in overweight and obese patients for each of the infections caused by the >60 pathogens for which the drug is indicated.

© 2016 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.

Figures

Figure 1
Figure 1
Log‐log relationship between weight and sulfamethoxazole pharmacokinetics (PKs). The natural logarithm (Ln) was used for the log‐transformation of values. Both weight in kilograms and body mass index (BMI), as well as sulfamethoxazole (SMX) PK parameters and concentrations, were log‐transformed following the method of Mandelbroit et al.30, 31 (a) Shows the relationship between elimination rate (and thus xenobiotic metabolism and excretion) and weight in patients >45.8 kg, which was three‐fourths. (b) Shows the slope of the relationships between the area under the concentration‐time curve (AUC), as derived by trapezoidal rule and weight, for which the log‐log slope was also three‐fourths. (c) Shows the relationship between volume and BMI in patients with BMI >16.2 kg/m2, that is above the multiple adaptive regression splines‐derived hinge. (d) Shows the relationship between BMI and peak SMX concentration, which showed a slope of three‐fourths on log‐log transformation, unlike the volume of distribution.
Figure 2
Figure 2
Log‐log relationship between weight and trimethoprim metabolism. The natural logarithm (Ln) was used for the log‐transformation of values. (a) Unlike sulfamethoxazole, the relationship between trimethoprim metabolism and weight in kilograms, did not obey the three‐fourths power laws, instead with a dimension of 0.61. (b) Similarly, body mass index vs. model‐derived elimination rate constant had a log‐log slope of 0.56. (c) Trapezoidal rule derived 0–24 hour area under the concentration‐time curve (AUC0–24) vs. weight regression revealed a log‐log slope that was virtually the same as for weight and elimination rate in panel a.
Figure 3
Figure 3
The relationship between body surface area and trimethoprim volume. The natural logarithm (Ln) was used for the log‐transformation of values. (a) A surprise was that body surface area was a predictor of trimethoprim volume of distribution, with a log‐log slope of four‐thirds or the inverse of three‐fourths. It would have been expected that these two parameters would be related by 1/length or height. (b) Interestingly, the observed peak concentration (amount of drug/volume of distribution) revealed a relationship characterized by the inverse of one‐fourth. Although these dimensions are unusual, they still, nevertheless, are part of the one‐fourth power laws.

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